A class of non-symmetric band determinants with the Gaussian q-binomialcoefficients
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A class of symmetric band matrices of bandwidth 2r+1 with the binomial coefficients entries was studied earlier. We consider a class of non-symmetric band matrices with the Gaussian q-binomial coefficients whose upper bandwith is s and lower bandwith is r. We give explicit formula for the determinant, the inverse (along with its infinity-norm when q -> 1) and the LU-decomposition of the class. We use the celebrated q-Zeilberger algorithm and unimodality property to prove claimed results.